State the condition under which the phenomenon of resonance occurs in series LCR circuit when ac voltage is applied. In a series LCR circuit, the current is in same phase with voltage. Calculate the value of self-inductance if the capacitor used in `20muF` and resistance used in 10 ohm with the ac source of frequency 50 Hz.

Explanation

Condition of resonance in a series LCR circuit:
`omegaL=1/(omegaC)`
where `omega`= angular frequency of the source, L=self inductance of the coil and C=capacitance.
Accordingly to the question, electric current and emf are in the same phase in the LCR circuit, i.e., the circuit is in the resonance condition.
Here, `omega=2pitimes50=2times3.14times50=314Hz`
`C=20muF=20times10^-6F=2times10^-5F`
Now, `omegaL=1/(omegaC)`
or, `L=1/(omega^2C)=1/((314)^2times(2times10^-5))=0.507 H`